Some solutions to problems are entirely mathematical while other problems are non-mathematical in nature and still others become mathematical after the true nature and scope of problem have been identified. The present invention relates to solving complex problems that arise in many different domains or fields of activity, and in some of which it is difficult to identify the parameters or factors that would be of interest in analyzing and solving the problem.
In the full contextual view, however, entire spheres of knowledge come into play. For example, what is true in the engineering context may not be ‘true’ in the manufacturing context. What is acceptable in an economic context may not be so in an ethical context. Yet the need for reliable context is a major imperative of our time, when information technology has empowered even the lowest-level worker with potential policy-level impact. At the same time, it is precisely information technology that makes large-scale contextual exploration feasible, linking diverse realms, both analytically and graphically.
Since the time of Descartes, scientific analysis has often been based on a system of independent, rectangular coordinates. The principal feature of this approach has been the projection of concrete ‘geometrical’ problems onto a set of independent ‘arithmetical’ dimensions. The benefit that accrues from that decomposition of spatial problems into numerical problems (and vice versa) is the ease with which the quantitative essentials of a phenomenon can be manipulated. Nevertheless, rectangular coordinates have no inherent geometry of their own. Each dimension is orthogonal to the others, which can be ‘N’ in number. No real articulation inheres in such an approach, other than the number of dimensions themselves. Any domain of significance must be defined after the fact. In conceptual studies, Cartesian coordinates are used only to create a uniform matrix of causal factors, all independent.
The contextual world, however, is not in general linearly independent. To adequately represent this realm requires a coordinate system with an inherent dimensionality of it own, so that cognitive units can be isolated and juxtaposed in illuminating fashion. In recent years, a number of partial approximations in this direction have come to light as;                a) A typology of form versus function as it applies to fish and their habit of swimming employed a triangular construct to organize the differences in fish shape and type of locomotion. Paul W. Webb, ‘Form and Function in Fish Swimming,” Scientific American        b) The inventor of the geodesic dome touted in print the virtues of triangular coordination, which he used in his architectural designs and claimed had merit in analytical pursuits. W. Buckminster Fuller, Collected Works        c) An English polymath has his own largely unpublished usages of a triangular analytic structure, including their application to the question of context. David Taylor (Malvern, England), personal correspondence        d) Authors in the field of ‘system theory’ have progressively expounded certain isolated principles necessary for a workable construct. Boulding, Churchman, Ackoff        
Neither separately nor together, however, do these offerings approach the full power and scope of my method.